The following work is an extension of an earlier publication on scalar diffraction of light. [ K. L. McDonald and F. S. Harris, J. Opt. Soc. Am. 42, 321 ( 1952)]. The present treatment pertains to the vector light field.
A new expression is given for the case of electromagnetic waves emitted by a simple harmonic Hertzian oscillator and diffracted by a thin black infinite half-plane immersed in a homogeneous and isotropic medium.
By use of Maggi’s transformation the problem is reduced to the evaluation of two integrals. Both integrals are approximated by the same method used in the scalar treatment. Two particular orientations of the oscillator are considered, and the six field components are written out for each case in terms of Fresnel integrals. Energy flow, relative intensity distribution, and polarization are discussed. The relative intensity is shown to agree with scalar predictions in the region of the shadow-boundary-plane, and therefore with experiment. The oscillator is infinitely removed from the diffracting edge, thereby allowing a comparison of the black screen with Sommerfeld’s perfectly reflecting screen.
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